Solitonic solutions for a variable-coefficient variant Boussinesq system in the long gravity waves

被引：12
作者：
Meng, De-Xin [1 ,2 ]
Gao, Yi-Tian [1 ,2 ,3 ]
Gai, Xiao-Ling [1 ,2 ]
Wang, Lei [1 ,2 ]
Yu, Xin [1 ,2 ]
Sun, Zhi-Yuan [1 ,2 ]
Wang, Ming-Zhen [1 ,2 ]
Lue, Xing [4 ]
机构：
[1] Beijing Univ Aeronaut & Astronaut, Minist Educ, Key Lab Fluid Mech, Beijing 100191, Peoples R China
[2] Beijing Univ Aeronaut & Astronaut, Natl Lab Computat Fluid Dynam, Beijing 100191, Peoples R China
[3] Beijing Univ Aeronaut & Astronaut, State Key Lab Software Dev Environm, Beijing 100191, Peoples R China
[4] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 215卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Lax pair; Variable-coefficient variant Boussinesq system; Nonlinear wave; Fluid dynamics; Solitonic solution; Darboux transformation; NONLINEAR SCHRODINGER-EQUATION; ION-ACOUSTIC-WAVES; SYMBOLIC-COMPUTATION; BACKLUND TRANSFORMATION; DARBOUX TRANSFORMATIONS; 1-SOLITON SOLUTION; MODEL; EVOLUTION; NEBULONS; DYNAMICS;
D O I：
10.1016/j.amc.2009.07.039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Variable-coefficient variant Boussinesq (VCVB) system is able to describe the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth. In this paper, with symbolic computation, a Lax pair associated with the VCVB system under some constraints for variable coefficients is derived, and based on the Lax pair, two sorts of basic Darboux transformations are presented. By applying the Darboux transformations, some solitonic solutions are obtained, with the relevant constraints given in the text. In addition, the VCVB system is transformed to a variable-coefficient Broer-Kaup system. Solitonic solutions and procedure of getting them could be helpful to solve the nonlinear and dispersive problems in fluid dynamics. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：1744 / 1751
页数：8
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